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Shapes of colloids matter at liquid interfaces. We explore the interactions between rough-surfaced nanocolloids at the air--water interface through the compaction of monolayers experimentally and numerically. Sufficiently rough systems exhibit a non-trivial intermediate state between a gas-like state and a close-packed jamming state due to roughness-induced capillary attraction. We also find that roughness-induced friction lowers the jamming point, and the tangential contact force owing to surface asperities can cause a gradual off-plane collapse of the compressed monolayer.